Geodesic
On a~complete orthonormal system
Sbornik. Mathematics, Tome 28 (1976) no. 3, pp. 315-324

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In this paper we construct in $L_2(0,1)$ a complete orthonormal system $\{\psi_n(x)\}_{n=1}^\infty$ for which every series $\sum_{n=1}^\infty c_n\psi_n(x)$ whose coefficients satisfy the condition $\sum_{n=1}^\infty c_n^2=\infty$ diverges on a set of positive measure. Bibliography: 6 titles. 
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     author = {B. S. Kashin},
     title = {On a~complete orthonormal system},
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     number = {3},
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     url = {http://geodesic.mathdoc.fr/item/SM_1976_28_3_a3/}
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B. S. Kashin. On a~complete orthonormal system. Sbornik. Mathematics, Tome 28 (1976) no. 3, pp. 315-324. http://geodesic.mathdoc.fr/item/SM_1976_28_3_a3/